1. Technical Field
This invention relates to electromagnetic machines, and more particularly to an improved design which reduces a given harmonic of the fundamental torque/displacement-angle relationship. While the invention is described, for convenience, as applied to rotary motors, it will be understood that it may be applied to linear motors, as well as to other electromagnetic machines having stationary and moving members, such as signal generating devices and electric power generators and other electric power producing devices. It has been found to be particularly useful when applied to rotary brushless DC, stepping and synchronous inductor motors.
2. Background Art
Rotary brushless DC, stepping, and synchronous inductor motors are well known in the art. Each type includes a rotor (moving member) and a stator (stationary member), with the stator having a plurality of salient poles energized by the passage of electric current through coils wound upon the poles. The coils are so arranged as to provide at least two electrical phases. The rotor includes at least one pair of N-S magnetic poles which are flux-linked with the stator poles, so that successive energizations of the phases provide rotary motion of the rotor.
The torque/displacement-angle of the rotor relationship, "torque/angle curve", between a rotor pole and each of the stator poles, may be expressed in general by the well known Fourier expansion: EQU T=k[1+A.sub.1 cos .theta..sub.e +A.sub.2 cos (2.theta..sub.e) . . . A.sub.n cos (n.theta..sub.e)+B.sub.1 sin .theta..sub.e +B.sub.2 sin (2.theta..sub.e) . . . +B.sub.n sin (n.theta..sub.e)],
where
T=torque, PA1 k=a constant, PA1 A.sub.1, A.sub.2 . . . A.sub.n=Fourier Coefficients (constants) of the cosine terms, PA1 B.sub.1, B.sub.2 . . . B.sub.n =Fourier Coefficients (constants) of the sine terms, and PA1 .theta..sub.e =the displacement of the rotor in electrical degrees.
In the above equation, A.sub.1 cos .theta..sub.e +B.sub.1 sin .theta..sub.e represents the fundamental (first) harmonic produced as the rotor poles pass the stator poles; A.sub.2 cos 2.theta..sub.e +B.sub.2 sin 2.theta..sub.e is the second harmonic of the fundamental; and so forth.
In the special case in which .theta..sub.e =o is defined as the rotor position for which the centerline of the rotor pole coincides with the centerline of the stator pole for which the Fourier expansion is being written, the expansion is greatly simplified to EQU T=K[B.sub.1 sin .theta..sub.e +B.sub.2 sin (2.theta..sub.e)+ . . . +B.sub.n sin (n.theta..sub.e)]
It is well known that the presence of torque/angle harmonics is especially detrimental to the performance of synchronous inductor motors, stepping motors, and brushless D.C. motors. In particular, a harmonic of the order corresponding to twice the number of phases (e.g. 4th harmonic for a 2-phase machine, 6th harmonic for a 3-phase machine, etc.) is particularly detrimental because of its dominance in the distribution of harmonic content. This particular harmonic is responsible for "detent torque", an objectionable resistance to rotation of the rotor of a de-energized motor. Step accuracy of a step motor, velocity modulation of synchronous inductor motors, stepping motors, and brushless D.C. motors, and microstepping ability of stepping motors and brushless D.C. motors are all adversely affected by torque/angle harmonics, and particularly by the one responsible for detent torque as described above.
It would be advantageous in such motors to be able to minimize the dominant harmonic which adversely affects motor performance as described above.
In copending Application Ser. No. 06/782,932, assigned to the assignee of the present application, there is disclosed means for minimizing a given harmonic the torque/angle curve of motors by providing a stator with two sets of poles, the sets of poles being nonuniformly spaced according to a specified relationship. While that arrangement satisfactorily reduces the undesired harmonic, the nonuniform stator slot widths cause certain complexities, the size of the stator coils is restricted practically by the narrowest slot, and the windings must be specially oriented with respect to the stator.